. THEORY OF STATISTICS. 
and D' and A will be comparable as regards age-distribution. 
There is obviously no difficulty in taking sex into account as well 
as age if necessary. The death-rates must be noted for each sex 
separately in every age-class and averaged with a system of 
weights based on the standard population. The method is also 
of importance for comparing death-rates in different classes of the 
population, e.g. those engaged in given occupations, as well as in 
different districts, and is used for both these purposes in the 
Decennial Supplements to the Reports of the Registrar General 
for England and Wales (ref. 16). 
19. Difficulty may arise in practical cases from the fact that 
the death-rates d, d, d;, . . . . are not known for the districts or 
classes which it is desired to compare with the standard popula- 
tion, but only the crude rates D and the fractional populations 
of the age-classes p; py, pg . . . . The difficulty may be partially 
obviated (cf. Chap. IV. § 9, pp. 51-3), by forming what is 
termed an sndex death-rate A’ for the class or district, A” being 
given by 
A=306p)¥ 4 aE 
t.e. the rates of the standard population averaged with the 
weights of the district population. It is the crude death-rate 
that there would be in the district if the rate in every age- 
class were the same as in the standard population. An 
approximate standardised death-rate for the district or class is 
then given by 
A 
Di=D rs (20) 
D” is not necessarily, nor generally, the same as D". It can 
only be the same if 
S(d.w) 3(o.w) 
(dp) 2(0p) 
This will hold good if, e.g., the death-rates in the standard 
population and the district stand to one another in the same 
ratio in all age-classes, s.e. 8,/d; = 8,/d,=0,/d; = etc. This method 
of standardisation is used in the Annual Summaries of the 
Registrar-General for England and Wales. 
Both methods of standardisation —that of § 18 and that of the 
present section—are of great and growing importance. They are 
obviously applicable to other rates besides death-rates, e.g. birth- 
rates (cf. refs. 17, 18). Further, they may readily be extended 
into quite different fields. Thus it has been suggested (ref. 19) 
that standardised average heights or standardised average weights 
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